[Estimation methods in a sampling survey]

Abstract

The objective of this paper is to present a guide for statistical analysis of a sampling survey. Advantages and disadvantages of classical sampling designs are first discussed. A sampling survey was designed to give more precise estimates of parameters which characterize a targeted well-defined population. Simple sampling design often is impossible in large population and rarely is the optimal solution. According to practical and economic constraints, and to available sampling frames, other strategies (stratification, unequal probabilities, several selection steps) may be necessary or more efficient. Fundamental tools to compute estimators and their confidence intervals are presented. The choice of the sampling method determine for each population unit the probability to include it in the final sample. These inclusion probabilities must be known to formulate estimators, ideally unbiased and with low variance. Difficulties arise from calculating the variance, especially for estimators which are not linear functions of the characteristics of interest. In that case, estimation procedures include Taylor linearization. It is always possible to find at least one linear estimator for a total. The total is the key-parameter in sampling theory, most parameters (such as ratios, means, percentages...), being function of unknown totals. Numerical examples are given.